It is well known that antitumorigenic substances composed of polysaccharides can be prepared by refining the extract obtained from extraction of the Basidiomycetes fungus with an aqueous solvent under normal pressure. The known process, however, has a serious disadvantage that the extraction method employed therein is intolerably poor in efficiency of extraction of the active components. The low extracting efficiency results in a considerable loss of the active components left over in great quantity in the extraction residue. This is quite undesirable not only from the viewpoint of productivity of the antitumorigenic substances but also from the viewpoint of loss of the valuable materials and of disposal of waste materials.